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Geographical threshold models were recently proven to have good results in scale-free networks generation [7].
This threshold condition is influenced by the geographical threshold models that are applied to scale-free network generation [7].
Actually, compared with the geographical threshold models, we use dot product to measure proximity of nodes instead of Euclidean distance.
The model derives from matrix factorization methods and geographical threshold models that were recently proven to show good results in generating scale-free networks.
In this paper, we investigate the representativeness of the synthetic Gabriel, geometric, population-weighted geographical threshold, and location-constrained Waxman graph models to the actual fibre backbone networks of six providers.
However, we will give not only mean-field approximations but also strict probabilistic proofs, which to the best of our knowledge have not been done for geographical threshold models yet and can be likely applied in the other works too.
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Conversely, the use of fixed geographical thresholds may lead to an overestimation of expected numbers in less densely populated areas, leading to a possible deflation of the clustering effect.
If clustering has arisen due to a geostationary exposure, then this could lead to detection only by the fixed geographical distance threshold.
We applied the K-function method for testing global space-time clustering using fixed geographical distance thresholds.
Use of fixed geographical distance thresholds may lead to an underestimation of expected numbers in more densely populated areas, leading to a possible inflation of the clustering effect.
To adjust for the effects of different population densities, the tests were repeated replacing geographical distance thresholds by distance to the Nth nearest neighbour, using all locations of all the cases in the data set except addresses for the same child at a different time.
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